I always find it surprising how little the Greek language has changed. As a modern Greek, I can easily understand the text from the Codex Sinaiticus image (apart from the damn wordsbeingwrittenlikethis)...
That's partially attributable to the legacy of Katharevousa, which was basically Ancient Greek with simplified grammare. During the two centuries of Katharevousa's official use, a LOT of heavily Ancient Greek-inspired vocabulary migrated in to the vernacular.